Answer:
(0.059, 0.133)
Step-by-step explanation:
Sample size = n = 250
Number of units which failed the test = x = 24
Proportion of units which failed the test = [tex]\frac{x}{n} = \frac{24}{250} =\frac{12}{125}[/tex] = 0.096
Proportion of units which did not fail the test = q = 1 - p = 1 - 0.096 = 0.904
Confidence level = 95%
z-value for the confidence level = z = 1.96
The true proportion of the components that fail to meet the specification would be:
[tex](p-z\sqrt{\frac{p \times q}{n}} , p+z\sqrt{\frac{p \times q}{n}})[/tex]
Using the values, we get:
[tex](0.096-1.96 \times \sqrt{\frac{0.096 \times 0.904}{250}} , 0.096+1.96 \times \sqrt{\frac{0.096 \times 0.904}{250}})\\\\ =(0.059,0.133)[/tex]
Thus, 95% confidence interval estimate for the true proportion of components, p, that fail to meet the specifications is (0.059, 0.133)
